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On subgroups of the multiplicative group of skew fields


Author: A. Lichtman
Journal: Proc. Amer. Math. Soc. 63 (1977), 15-16
MSC: Primary 20H20; Secondary 16A18
DOI: https://doi.org/10.1090/S0002-9939-1977-0447432-0
MathSciNet review: 0447432
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Abstract: We give an example of a skew field D for which the multiplicative group $ {D^ \ast }$ of D contains a finitely generated subgroup which satisfies a nontrivial identity and has no solvable normal subgroup of finite index. It gives a negative answer to a question of S. Bachmuth.


References [Enhancements On Off] (What's this?)

  • [1] J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250-270. MR 44 #4105. MR 0286898 (44:4105)
  • [2] Proceedings of the Second International Conference on the Theory of Groups, (Canberra, Australia, 1973), Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin and New York, 1974. MR 49 #9054. MR 0344315 (49:9054)
  • [3] A. I. Lichtman, On embedding of group rings in division rings, Israel J. Math. 23 (1976), 288-297. MR 0432692 (55:5678)
  • [4] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Vols. 1, 2, Springer-Verlag, Berlin and New York, 1972. MR 48 #11314, 11315.
  • [5] G. Baumslag, Wreath products and extensions, Math. Z. 81 (1963), 286-299. MR 27 #1503. MR 0151518 (27:1503)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0447432-0
Keywords: Multiplicative group of division ring, group ring
Article copyright: © Copyright 1977 American Mathematical Society

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